Polyhydroxyalkanoic acid (PHA) is a polyester which microorganisms accumulate in the cell. In recent years, PHA is attracting attention not only as a biodegradable plastic material but also as a plastic material derived from biomass. The most common PHA is a homopolymer (hereinafter referred to as “P(3HB)”) having (R)-3-hydroxybutanoic acid (3HB) as the building block. However, P(3HB) has drawbacks that it is highly crystallizable and lacks flexibility. Thereafter, a method of producing a PHA copolymer (hereinafter referred to as “P(3HB-co-3HHx)”) consisting of 3HB and (R)-3-hydroxyvaleric acid (3HV) using Ralstonia eutropha having a high PHA-accumulating potential, was developed (Kokai (Japanese Unexamined Patent Publication) No. 57-150393, or Kokai (Japanese Unexamined Patent Publication) No. 59-220192). There was little enhancement in flexibility, since 3HB and 3HV cocrystallize.
In recent years, a method of producing a copolymer (hereinafter referred to as “P(3HB-co-3HHx)”) consisting of 3HB and (R)-3-hydroxyhexanoic acid (3HHx) was developed, which enabled the production of a highly flexible polyhydroxyalkanoic acid (Kokai (Japanese Unexamined Patent Publication) No. 5-93049, or Kokai (Japanese Unexamined Patent Publication) No. 7-265065). In the methods described in these publications, P(3HB-co-3HHx) is produced from a plant oil by means of a soil bacterium Aeromonas caviae. 
The inventors of the present invention reported that a copolymer (hereinafter referred to as “P(3HB-co-3HA)” wherein 3HA is a C4-C12 (R)-3-hydroxyalkanoic acid) consisting of 3HB and (R)-3-hydroxyalkanoic acid (3HA) can be produced from a plant oil by means of a recombinant in which a mutant of PHA synthetase gene derived from Pseudomonas sp. was inserted into a deletion mutant (PHB−4 strain) of PHA synthetase gene derived from Ralstonia eutropha (Kokai (Japanese Unexamined Patent Publication) No. 2007-125004).
On the other hand, homopolymers and copolymers thereof comprising as the building blocks 3-hydroxyalkanoic acid having branched alkyl groups have been reported (Int. J. Biol. Macromol., 1990, Vol. 12, pp. 92-101). However, generally, in the production of polymers comprising as the building blocks 3-hydroxyalkanoic acid having branched alkyl groups, difficulty in controlling monomer composition makes difficult the synthesis of a polymer in terms of the physical properties of the material, and in said publication as well, the branched alkyls are limited to branched octanoic acid and the physical properties were not disclosed.